A circle has a radius of ${6}$. An arc in this circle has a central angle of $48^\circ$. What is the length of the arc? Either enter an exact answer in terms of $\pi$ or use $3.14$ for $\pi$ and enter your answer as a decimal. ${48^\circ}$ ${6}$
Solution: First, calculate the circumference of the circle. ${48^\circ}$ ${6}$ ${12\pi}$ ${c} = 2\pi r = 2\pi ({6}) = {12\pi}$ The ratio between the arc's central angle ${\theta}$ and $360^\circ$ is equal to the ratio between the arc length ${s}$ and the circle's circumference ${c}$. $\dfrac{{\theta}}{360^\circ} = \dfrac{{s}}{{c}}$ $\dfrac{{48}^\circ}{360^\circ} = \dfrac{{s}}{{{12\pi}}}$ $\dfrac{2}{15} = \dfrac{{s}}{{12\pi}}$ $\dfrac{2}{15} \times {12\pi} = {s}$ $\dfrac{8}{5}\pi = {s}$ ${48^\circ}$ ${6}$ ${12\pi}$ ${\dfrac{8}{5}\pi}$